Question
Rationalize the denominator. \[ \frac{\sqrt{2}}{\sqrt{11}} \]
Ask by Reyes Reed. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The rationalized form is \( \frac{\sqrt{22}}{11} \).
Solution
Calculate or simplify the expression \( \frac{\sqrt{2}}{\sqrt{11}} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{\sqrt{2}}{\sqrt{11}}\)
- step1: Multiply by the Conjugate:
\(\frac{\sqrt{2}\times \sqrt{11}}{\sqrt{11}\times \sqrt{11}}\)
- step2: Multiply the numbers:
\(\frac{\sqrt{22}}{\sqrt{11}\times \sqrt{11}}\)
- step3: Multiply the numbers:
\(\frac{\sqrt{22}}{11}\)
The rationalized form of the given expression \(\frac{\sqrt{2}}{\sqrt{11}}\) is \(\frac{\sqrt{22}}{11}\).
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Simplify this solution The Deep Dive
To rationalize the denominator of the expression \(\frac{\sqrt{2}}{\sqrt{11}}\), you multiply both the numerator and the denominator by \(\sqrt{11}\): \[ \frac{\sqrt{2}}{\sqrt{11}} \times \frac{\sqrt{11}}{\sqrt{11}} = \frac{\sqrt{2} \cdot \sqrt{11}}{\sqrt{11} \cdot \sqrt{11}} \] This simplifies to: \[ \frac{\sqrt{22}}{11} \] So the rationalized form of the expression is \(\frac{\sqrt{22}}{11}\).
